This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonli...This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.展开更多
We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations an...We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.展开更多
基金supported by the National Natural Science Foundation of China(Nos.10921101,11471190)the Shandong Provincial Natural Science Foundation of China(No.ZR2014AM002)the Programme of Introducing Talents of Discipline to Universities of China(No.B12023)
文摘This paper deals with backward stochastic differential equations with jumps,whose data(the terminal condition and coefficient) are given functions of jump-diffusion process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential equations, and then obtains a new type of nonlinear Feynman-Kac formula related to such BSDEs with jumps under some regularity conditions.
基金support by Deutsche Forschungsgemeinschaft through the Research Training Group RTG 1953.
文摘We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.
